That or Is the shield between your office badge reader and the office card? It may not be encasing your card, but if it’s between the card and reader, it may block the signal. Definitely a good idea to try it with the shield in place in the wallet but the Tesla card out of your wallet.
I have my office badge (an older badge system from HID) and the Tesla card in my card wallet (repurposed business card holder that contains those two cards and 4 credit cards). I had to separate the two into opposite sides of the card holder. When the cards were directly next to each other, neither worked. When the cards are separated by the credit cards and the fabric of the wallet pouches, the office badge can be read while the wallet is still folded and by holding either face to the reader. However, I have to unfold the card wallet and really separate the two cards for the Tesla card to be read. Easy enough to do once a month when I’m demoing the car to someone and want to show off the rfid card. Otherwise, the Tesla card never gets used.
Long way of saying you also might need to separate the two cards in your wallet (one in the right side, one in the left side) and even possibly need to unfold your wallet for one/both of them to be read.